cot B = 12/5, prove that : tan²B - sin²B = sin⁴B sec²B
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tan^2B=sin^2B/cos^2B
tan^2B=sin^2B/cos^2B
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cot b = 12/5 ⇒ tan b = 5/12 ⇒ sin b = 5/13 [Using Pythagoras theorem] ⇒ sec b = 13/12 LHS = tan2 b - sin2 b = (5/12)2 - (5/13)2 = 52/122 - 52/132 = 52 [1/122 - 1/132] = 52[(132 - 122) / 122.132] = 52[(52) / 122.132] = 54 / (122.132) RHS = sin4 b x sec2 b = (5/13)4 x (13/12)2 = (54/134) x (132/122) = 54 / (132.122) ∴ LHS = RHS Hence proved.
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